Project Sedenion

We propose a fundamental restructuring of deep learning architectures based on the prin-ciples of Axiomatic Physical Homeostasis (APH). Current state-of-the-art models (Trans-formers) rely on Rank-2 tensor operations (matrix multiplication), limiting them to strictlyassociative linear representations. We demonstrate that the phenomenon of Grokking—delayed generalization far past the point of overfitting—is physically isomorphic to a Geo-metric Phase Transition from a high-entropy Sedenion state to a low-entropy Octonionictiling. We introduce the Rank-3 Tensor Network, a neural architecture designed toexplicitly compute the Associator Anomaly [x, y, z]. By replacing weight decay withStiffness Regularization, we propose a path toward Artificial General Intelligence (AGI)that operates not by statistical correlation, but by geometric necessity.